New, and wondering if this sounds like a narc?

i recently broke up with my suspected narc of 2 years. we lived together most of that time, and i have 2 kids, not from him. Countless times ive caught him with very inappropriate encounters with other females, 2 times which led to me throwing him out, and then eventually feeling like i cannot live without him, and then getting him back. most recently, i came to find, through probably a very unethical way (spy software on my computer) that he was going on "private browsing" and looking up weird porn-pregnancy porn, and by me pretending to know more than i actually did, i got him to confess that he was on other porn sites (despite swearing countless times that he does not do that, and me telling him that it makes me feel horrible about myself) and he also confessed "looking up" some girl that he had met up with last summer, after he claimed that time was a dumb decision etc etc... before i confronted him, he looked me dead in the eye and swore on my kids,(who he really adores when hes in a good mood) and swore on "everything sacred" that he hasnt been on porn or private browsing etc etc. Total lied right to my face.
Over the course of our relationship, i found out he was taking pills every thursday while i was at work,(He worked from home) just to "prove that i cant tell him what to do". when i found out, he stopped,and began therapy. several weeks ago, he commented that his therapist told him he was a narcissist, but then realized he shouldnt have told me that. I feel so insecure, that he was always looking at other girls. i used to tell him that he would walk into a room and immediately look around at who is looking at him. He is always the smartest person in the room, a real intellectual, or so he thinks. very charismatic and charming and good looking, but behind closed doors i would always hear him say how fat he was like 100 times a day, and have major hang ups about his penis size, and whether or not he satisfies me with it. He has extreme rage, that gets so severe he throws or slams things. toward the end, he threw his phone in my stomach because i wanted to look through it. he would always say things like "yes mom" to me, was very condescending, called me a "cunt" and "stupid bitch" quite a few times, and sometimes in front of my kids. he would get often snappy with them too, and display extremes- exceptionally loving, or very low patient/anger.
I finally had enough when i caught him last week. today is monday, and he has been gone since last wednesday. i got all his stuff out of the house the same day, deleted all pics and messages etc.we had a few text conversations before the light was shed on me that he was a possible narc, where he said "lets face it, you were just waiting to catch me doing something, so it was bound to happen", but other times sounded like he was really deeply sorry, and that he wished it would have worked out. He hasnt seemed at all like he's trying to get me back or anything, but he emailed my daughter a few times, the last of which was a "farewell" sounding letter. i think he knows this is for good. but on the flipside, I SEVERELY miss him. there were so many good things about him that i loved. he was my best friend and the closest person to me. he would really try to help make my life easier, buy me nice things, help around the house a lot, was always with me and by my side, and we had great sex until the very end. i just know this is impossible. he has lied and cheated countless times, and i know he cannot change. also, his father is sort of like this. he cheated on his mother with a woman down the block from them when my ex was 10. He ended up marrying the woman and moving in down the block! appalling. Obviously they are no longer together, but now he's dating my ex's gradmothers late husbands grandaughter (on my ex's mothers side, so they're not related) . weird wild situation. the girl is 20, my ex's dad is 58. my ex has major dad issues, always looking to please him. I know you cannot diagnose, but do you think this sounds like a narc? im so lost. thank you. PS- im 33 and hes 25.